Between 1919 and 1958, Adomeit exhibited his artwork in 40 consecutive May Shows. His works were also accepted into other juried exhibitions including the Pennsylvania Academy of Fine Arts, the Corcoran Gallery's biennial exhibitions, and Carnegie International Exhibition of 1930.
An active member and proponent of the Cleveland arts community, Adomeit along with Charles Shackleton founded the Cleveland Society of Artists. The society held numerous events and programs, and organized an annual auction to finance scholarships to the Cleveland School of Art.
Adomeit started his career as a lithographic apprentice. After a few years, he and a colleague purchased the Mason Engraving Co. renaming it Caxton Engraving Co., later simply Caxton Co.. Adomeit rose to be president and director before retiring in 1956. Adomeit married Ida Von Den Steinen and their daughter Ruth Adomeit was a noted collector of miniature books.